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Re: Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. [#permalink]
3
Use the weighted average formula to get the ratio of Fiber X to Fiber Max:
[0.55X+0.70m][/x+m] = 0.65
where x is the amount of Fiber X and m is the amount of Fiber Max.
This is not that different from the regular average formula—on the top, there is the total amount of
fiber (55% of Fiber X and 70% of Fiber Max), which is divided by the total amount of cereal (x + m)
to get the average. Simplify by multiplying both sides by (x + m):
0.55x + 0.70m = 0.65(x + m)
0.55x + 0.70m = 0.65x + 0.65m
To simplify, multiply both sides of the equation by 100 to eliminate all the decimals:
55x + 70m = 65x + 65m
55x + 5m = 65x
5m = 10x
m/x= 1/2
Since m and x are in a 2 to 1 ratio, 2/3 of the total is m and 1/3 of the total is x. Since the total is 12
ounces, Fiber X accounts for (12) = 4 ounces of the mixed cereal.
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Re: Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. [#permalink]
One shortcut to this procedure is to note that the weighted average (65%) is 10% away from Fiber
X’s percent and 5% away from Fiber Max’s percent. Since 10 is twice as much as 5, the ratio of the
two cereals is 2 to 1. However, it is a 2
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Re: Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. [#permalink]
Is there a non-alligation way to solve?
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Re: Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. [#permalink]
3
Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon combines an amount of the two cereals in a single bowl of mixed cereal that is 65% fiber. If the bowl contains a total of 12 ounces of cereal, how much of the cereal, in ounces, is Fiber X?

X----------------------Max
55---------65----------70
65-55=10----------70-65=5

Write in cross direction:
x/m = 5/10
10x=5m
x=5/10m
or m = 2x

Given,
x+m=12
x+2x=12
3x=12
x=4
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Re: Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. [#permalink]
3
I think math do the talks and no need for explanation ( if any part remains unclear feel free to ask) :

0.55X + 0.7 M = 12 * 0.65
X+M=12 hence M=12-X
So: 0.55 X + 0.7 ( 12 - X ) = 7.8
0.55 X + 8.4 - 0.7 X = 8.4
0.15 X = 0.6
=====> X= 0.6/0.15 = 4
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Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. [#permalink]
1
Farina wrote:
Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon combines an amount of the two cereals in a single bowl of mixed cereal that is 65% fiber. If the bowl contains a total of 12 ounces of cereal, how much of the cereal, in ounces, is Fiber X?

X----------------------Max
55---------65----------70
65-55=10----------70-65=5

Write in cross direction:
x/m = 5/10

We can do the second half in an alternative method as well:
x:m:t = 5:10:15
x/t = 5/15 (= 1/3)

Given amount of fiber, t=12 ounces
Therefore, we can calculate the amount of fiber as well: Ratio * t = (x/t) * t = (1/3) * 12 = 4 ounces


You choose your favourite method!
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Re: Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. [#permalink]
1
Here,
x=55%,m=70% & combined 65%
That means x:m=2:1, x=(1/3)*Total
Given total 12.
Now need x= (1/3)*12=4 Answer(B)
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Re: Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. [#permalink]
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